Problem A Pole vaulting - a story of harmonious combination between man and pole
问题 A 撑杆跳 - 人与撑杆和谐结合的故事

Pole vault is considered one of the most difficult sports. The 6.14-meter world record set by Ukrainian pole vaulter Bubka in 1994 was once considered one of the records to break most hardly, but now the record has been repeatedly broken. On August 25th of this year, at the Silesia station of the World Association of Athletics Federations Diamond League, Swedish pole vault world record holder Duplandis broke his own 6.25-meter jump at the Paris Olympics with an astonishing 6.26-meter result and won the gold medal. In fact, Duplandis has broken his own world records multiple times.
撑杆跳被认为是最困难的运动之一。乌克兰撑杆跳运动员布布卡在 1994 年创造的 6.14 米世界纪录曾被认为是最难打破的纪录之一，但现在这个纪录一再被打破。今年8月25日，在世界田径联合会钻石联赛西里西亚站，瑞典撑杆跳世界纪录保持者杜普兰迪斯以惊人的6.26米的成绩打破了自己在巴黎奥运会上跳出的6.25米纪录，夺得金牌。事实上，杜普兰迪斯已经多次打破了他自己的世界纪录。

Technically speaking, pole vaulting involves several main processes, including "Approach Run, plant, takeoff, swing, and clearance ", which are not only related to the athlete's physical features and ability, but also closely related to the pole used. Your team is requesting solutions to the following issues:
从技术上讲，撑杆跳涉及几个主要过程，包括“进场跑、植、起、摆、过关”，这些过程不仅与运动员的身体特征和能力有关，也与所使用的撑杆密切相关。您的团队正在请求以下问题的解决方案：

(1) Collect relevant data, including some physical parameters of athletes, as well as data on the material, mechanical characters, and performance of the poles used.
（1） 收集相关数据，包括运动员的一些身体参数，以及所用杆的材料、机械特性和性能的数据。

(2) Establish a mathematical model for the pole vault process and calculate the athlete's performance based on the aforementioned parameters.
（2） 建立撑杆跳过程的数学模型，并根据上述参数计算运动员的表现。

(3) Study the relation between the grades and length, material of pole, etc., and also consider the effect on heights, weights, genders and speed of player.
（3） 研究等级与长度、杆子材质等之间的关系，并考虑对球员身高、体重、性别和速度的影响。

(4) Write a short report recommending poles for players with different levels.
（4） 写一份简短的报告，为不同级别的玩家推荐钢管。

Problem B If you spot a lantern fly…
问题 B 如果您发现灯笼飞......

Spotted lanternflies (Lycorma delicatula) are insects from Asia that are quickly spreading in North America and have a growing negative effect on agricultural production. Since their arrival to the USA about ten years ago, they have now spread to at least 16 states (PA, NY, NJ, MD, MI, OH, IN, WV, VA, NC, DE, CT, RI, MA, KY, TN). These insects are particularly dangerous for grapevines, which is becoming a major concern for many vineyards and wineries present in NY State. Spotted lanternflies feast on plant’s sap and remove so much of it that the vine has far lower chances of surviving the cold temperatures. Even if a seriously affected vine survives, it is much less likely to produce any grapes next season. Quarantine measures in several states and public eradication campaigns have not proven successful in eliminating this threat. Most scientists expect the spread to continue until the lanternflies face off with some natural predators– either those already keeping the lanternfly population limited in Asian countries1 or the native US birds and insects once they recognize the spotted lanternflies as suitable food. Either way, this process will take at least 5-10 years and for now the goal is to slow down the spread (e.g., through quarantine measures) and limit the immediate economic impact (e.g., by treating vines with insecticides).
斑点灯笼蝇 （Lycorma delicatula） 是来自亚洲的昆虫，在北美迅速传播，对农业生产的负面影响越来越大。自从大约十年前抵达美国以来，它们现在已经传播到至少 16 个州（宾夕法尼亚州、纽约州、马里兰州、密歇根州、俄亥俄州、印第安纳州、西弗吉尼亚州、北卡罗来纳州、德国、CTRI、马萨诸塞州、KYTN）。这些昆虫对葡萄藤特别危险，这正在成为纽约州许多葡萄园和酿酒厂的主要关注点。斑点灯笼蝇以植物的汁液为食，并去除了如此多的汁液，以至于葡萄藤在寒冷温度下存活的机会要低得多。即使受到严重影响的葡萄藤存活下来，下个季节生产葡萄的可能性也要小得多。一些州的检疫措施和公共根除运动尚未证明能成功消除这一威胁。大多数科学家预计，这种传播会持续到灯笼蝇与一些天敌对峙——要么是那些已经在亚洲国家限制灯笼蝇种群数量的人1，要么是美国本土的鸟类和昆虫，一旦他们认识到斑点灯笼蝇是合适的食物。无论哪种方式，这个过程至少需要 5-10 年，目前的目标是减缓传播（例如，通过检疫措施）并限制直接的经济影响（例如，用杀虫剂处理葡萄藤）。

Your team is asked to address the following two challenge problems.
您的团队需要解决以下两个挑战问题。

In addition to your detailed manuscript, please provide a one-page executive summary for the members of the Integrated Pest Management Program . While highlighting your recommendations, please make sure to also address the limitations of your modeling approach and possible directions for future improvement.
除了您的详细手稿外，请为综合害虫管理计划的成员提供一页的执行摘要。在强调您的建议的同时，请确保还解决建模方法的局限性以及未来可能的改进方向。

Challenge 1: Limiting the spread in NY State
挑战 1：限制纽约州的传播

Spotted lanternflies (SLF) hatch from eggs & start their life as nymphs in April, become adults by late July, lay their eggs in September-November, and then die in December. Each female SLF usually lays at least one “eggmass” with about 35 eggs in it.
斑点灯笼蝇（SLF）从卵中孵化出来，四月开始以若虫的形式生活，七月晚些时候成为成虫，九月至十一月产卵，然后在十二月死亡。每个雌性 SLF 通常至少产下一个“卵块”，里面大约有 35 个卵。

SLF can feed on more than 100 different plants (which makes it much easier for them to spread), but their all-time favorite is the so-called “Tree of Heaven” (Ailanthus altissima). If it is present in the vicinity, the lanternflies are known to lay about 7 times as many eggs as usual. Thus, removing these trees (present in Ithaca and, more broadly, in the Finger Lakes region) may be one of the most effective anti-SLF measures. But some of the current guidelines recommend using a “tree trap” approach; i.e., removing only small Trees of Heaven while treating the larger ones with a long lasting insecticide (dinotefuran) to kill the returning SLF.
SLF 可以以 100 多种不同的植物为食（这使得它们更容易传播），但它们一直以来最喜欢的是所谓的“天堂之树”（Ailanthus altissima）。如果它出现在附近，已知灯笼蝇产下的卵大约是平时的 7 倍。因此，移除这些树木（存在于伊萨卡岛，更广泛地分布在五指湖地区）可能是最有效的抗 SLF 措施之一。但目前的一些指导方针建议使用 “树木陷阱” 方法;即，只移除小的天堂树，同时用长效杀虫剂（呋虫胺）处理较大的树木以杀死返回的 SLF。

SLF cannot fly too far on their own – the natural distance they can cover in one year is estimated to be between 4 and 10 miles only. But the spread becomes much faster when they lay the eggmass on shipping materials, railroad cars, or automobiles, which by April, when the eggs hatch, can be in a very different location. Thus, the quarantine measures are usually focused on finding and destroying the eggmasses before they have a chance to travel far.
SLF 不能自己飞得太远——它们在一年内可以行驶的自然距离估计仅在 4 到 10 英里之间。但是，当它们将卵块产在运输材料、铁路车厢或汽车上时，传播速度会快得多，到 4 月，当卵孵化时，这些卵可能位于非常不同的位置。因此，检疫措施通常侧重于在蛋团有机会远行之前找到并销毁它们。

You need to model the SLF population spread in NY State and suggest the best strategy for slowing it down. Regular inspections of vehicles & railroad cars require resources (money, time, coordination with businesses and agencies, human efforts), which could be otherwise spent on other measures – e.g., on reducing the number of Trees of Heaven (TOH) or setting up “tree traps”. Suggest a strategy for balancing these efforts. Explain the predicted effect on the overall SLF population as well as the economic and environmental impact in the next five years.
您需要对纽约州的 SLF 种群传播进行建模，并提出减缓其速度的最佳策略。定期检查车辆和铁路车厢需要资源（金钱时间、与企业和机构的协调、人力努力），这些资源本可以用于其他措施 - 例如，减少天堂树（TOH）的数量或设置“树木陷阱”。建议平衡这些工作的策略。解释对整体 SLF 种群的预测影响以及未来五年的经济和环境影响。

Challenge 2: Saving the grapes and/or saving the vines?
挑战 2：拯救葡萄和/或拯救葡萄藤？

● In the Spring: at least 15-20 nymphs per vine before you spray (one application should be enough).
● 春季：喷洒前每棵葡萄藤至少 15-20 株若虫（一次使用就足够了）。

● In August-September, when the adult SLF are migrating and many of them move to vineyards: at least 5-10 adult SLF per vine before you spray (repeated applications might be needed).
● 8 月至 9 月当成年 SLF 迁移，其中许多转移到葡萄园时：喷洒前每棵葡萄树至少 5-10 只成年 SLF（可能需要重复施用）。

All insecticides have different effectiveness against the SLF, but also come with different restrictions: on the maximum dose that can be used per year and on the Pre-Harvest Intervals (PHI) – i.e., the number of days that has to pass after the last application before you are allowed to harvest the grapes.
所有杀虫剂对 SLF 的疗效都不同，但对每年可以使用的最大剂量和收获前间隔 （PHI） 也有不同的限制——即在最后一次施药后必须经过的天数才能被允许收获葡萄。

This presents a hard dilemma when the adult lanternflies arrive close to the harvest time.
当成年灯笼蝇接近收获时间到达时，这就带来了一个艰难的困境。

If you start using insecticides, you will likely have to harvest later than intended, which increases the potential incidence and severity of fungal diseases, resulting in reduced yield as well as reduced grape quality. On the other hand, if you decide to wait with the insecticide until after the harvest, you risk long-term damage to your vines due to SLF sap feeding.
如果您开始使用杀虫剂，您可能不得不比预期晚收割，这会增加真菌病的潜在发病率和严重程度，导致产量下降和葡萄质量下降。另一方面，如果您决定等到收获后才使用杀虫剂，则可能会因 SLF 汁液喂养而对葡萄藤造成长期损害。

Suggest an optimal strategy for using insecticides throughout the season. Among other measures, this might involve changing the threshold of observed SLF (nymphs and adults) before you spray or, more generally, making that threshold depend on
建议在整个季节使用杀虫剂的最佳策略。除其他措施外，这可能涉及在喷洒之前更改观察到的 SLF（若虫和成虫）的阈值，或者更一般地说，使该阈值取决于

● SLF migration patterns,
● SLF迁移模式，

● the number of days remaining until the harvest,
● 距离收获还剩多少天，

● the chemicals already used up to that point, and/or
● 截至那时已经使用的化学品，和/或

● the predicted weather (which influences the development of fungal diseases).
● 预测的天气（影响真菌病害的发展）。

In addition to financial considerations, please also address a possible impact of your approach on other (beneficial) insects.
除了财务考虑外，还请说明您的方法可能对其他（有益）昆虫产生的影响。

Problem C The Federal Reserve Raises Interest Rates
问题 C美联储提高利率

In 2023, the Federal Reserve basically continued the aggressive interest rate hike policy of the previous year, holding a total of 8 monetary policy meetings throughout the year Among them, there were four interest rate hikes in January, March, May, and July meetings, each by 25 basis points. The US federal funds rate reached 5.25% to 5.5%, the highest level in 22 years.
2023 年，美联储基本延续了上一年的激进加息政策，全年共召开了 8 次货币政策会议，其中，1 月、3 月、5 月和 7 月共加息 4 次，每次加息 25 个基点。美国联邦基金利率达到 5.25% 至 5.5%，为 22 年来的最高水平。

The Federal Reserve's aggressive interest rate hikes continue to disrupt the world economy. First, the aggressive interest rate increase policy has led to the soaring yield of long-term U.S. treasury bond bonds, increased the cost of auto loans, credit card lending and various forms of commercial loans, raised the cost of living of U.S. residents, and severely squeezed small and medium-sized banks from the asset side and the liability side, leading to financial risks; Secondly, the aggressive interest rate hike policy has generated strong spillover effects. It has driven the strengthening of the US dollar, prompted international capital to flow massively from emerging markets to the United States in pursuit of higher returns, continuously compressed the monetary policy space of other economies, and forced many countries to make more difficult choices between cross-border capital flows, monetary policy independence, and exchange rate stability; Thirdly, aggressive interest rate hikes have increased the debt servicing costs of emerging markets and developing economies, leading to currency weakness in some economies, making their economic growth prospects even more bleak, exacerbating global financial market turbulence, and hindering the recovery process of the world economy.
美联储激进的加息继续扰乱世界经济。首先，激进的加息政策导致美国长期国债收益率飙升，增加了汽车贷款、信用卡贷款和各种形式的商业贷款的成本，提高了美国居民的生活成本，从资产端和负债端严重挤压了中小银行， 导致财务风险;其次，激进的加息政策产生了强大的溢出效应。它带动了美元的走强，促使国际资本为追求更高的回报而从新兴市场大量流向美国，不断压缩其他经济体的货币政策空间，迫使许多国家在跨境资本流动、货币政策独立、汇率稳定之间做出更加艰难的选择;第三，激进的加息增加了新兴市场和发展中经济体的偿债成本，导致一些经济体货币疲软，使其经济增长前景更加黯淡，加剧了全球金融市场的动荡，阻碍了世界经济的复苏进程。

At the monetary policy meeting in December 2023, the Federal Reserve announced that the target range for the federal funds rate would remain unchanged between 5.25% and 5.5%. Federal Reserve Chairman Powell said at a press conference after the meeting that the current federal funds rate "may be close to the peak of this tightening cycle," and attending Fed officials generally believe that "further interest rate hikes are unlikely to be appropriate," but they also do not want to rule out this possibility.
在 2023 年 12 月的货币政策会议上，美联储宣布联邦基金利率的目标区间将保持在 5.25% 至 5.5% 之间不变。美联储主席鲍威尔在会后举行的新闻发布会上表示，目前的联邦基金利率“可能接近本轮紧缩周期的峰值”，与会的联储局官员普遍认为“进一步加息不太可能合适”，但他们也不想排除这种可能性。

Analysts believe that it is not easy for the Federal Reserve to control a reasonable shift in monetary policy. On the one hand, the Federal Reserve still faces the "last mile" challenge of combating inflation; On the other hand, it is necessary to ensure the flexibility of monetary policy and avoid overcorrection. During the policy shift, it may also have an impact on the global financial market and bring more uncertainty to the world economy.
分析人士认为，美联储要控制货币政策的合理转变并不容易。一方面，美联储仍然面临对抗通胀的“最后一英里”挑战;另一方面，要保证货币政策的灵活性，避免矫枉过正。在政策转变期间，也可能对全球金融市场产生影响，给世界经济带来更多不确定性。

In September 2024, the Federal Reserve unexpectedly announced a rate cut, causing global capital markets to flock to the Chinese stock market. In early October, the unexpected non farm payroll data released by the United States once again left the market confused. Will the Federal Reserve raise interest rates again? Can the Chinese market continue to attract global capital? How will the future of the global market go?
2024 年 9 月，美联储出人意料地宣布降息，导致全球资本市场涌向中国股市。10月初，美国意外公布的非农就业数据再次让市场感到困惑。美联储会再次加息吗？中国市场能否继续吸引全球资本？全球市场的未来将如何发展？

Consider the background information and address the following:
考虑背景信息并解决以下问题：

(1) In history, the Federal Reserve has adopted strategies of raising or lowering interest rates at different times. Please choose appropriate indicators, collect data, establish a model to predict the Fed's strategy of raising or lowering interest rates, and discuss the effectiveness and accuracy of the model;
（1） 历史上，美联储在不同时期采取了加息或降息的策略。请选择合适的指标，收集数据，建立模型来预测美联储的加息或降息策略，并讨论模型的有效性和准确性;

(2) Please establish a model to analyze the monetary policy that China will adopt when the Federal Reserve implements a rate hike or cut strategy. And what kind of impact will the policies adopted by China have on the national economy. Among them, please choose appropriate indicators to characterize the specific impact.
（2） 请建立一个模型来分析当美联储实施加息或降息策略时中国将采取的货币政策。中国采取的政策将对国民经济产生什么样的影响。其中，请选择适当的指标来描述具体影响。

(3) Please establish a model to describe the impact of the Federal Reserve's interest rate hike or rate cut strategy on the world economy after a period of time (such as one year)? What strategies should major economies (such as the European Union, ASEAN, Japan, and South Korea) adopt to overcome this impact? What is the impact on the economy?
（3） 请建立一个模型来描述一段时间后（例如一年）美联储的加息或降息策略对世界经济的影响？主要经济体（如欧盟、东盟、日本和韩国）应采取哪些策略来克服这种影响？对经济有什么影响？

Problem D Scheduling and Path Optimization for Autonomous Cleaning Vehicles on Campus
问题 D园区自主清洁车的调度和路径优化

As campus sizes continue to expand, the challenges of environmental sanitation management have become increasingly prominent. Traditional manual cleaning methods are not only inefficient but also susceptible to factors such as weather and personnel arrangements, making it difficult to maintain cleanliness on campus. To address this issue, many universities have started to adopt smart technologies, with autonomous cleaning vehicles emerging as a new cleaning tool that is gradually gaining attention.
随着园区规模的不断扩大，环境卫生管理的挑战日益突出。传统的人工清洁方法不仅效率低下，而且容易受到天气和人员安排等因素的影响，难以保持校园清洁。为了解决这个问题，许多大学已经开始采用智能技术，自动清洁车成为一种新的清洁工具，逐渐受到关注。

These autonomous cleaning vehicles utilize advanced sensors and navigation systems to automatically identify cleaning areas, avoid obstacles, and plan their routes, thereby efficiently completing cleaning tasks. Their advantages include 24/7 operation, reduced labor costs, and improved cleaning efficiency. However, effectively scheduling multiple autonomous cleaning vehicles and reasonably planning their cleaning paths to meet the cleanliness needs of different campus areas at various times remains a pressing challenge.
这些自动清洁车利用先进的传感器和导航系统来自动识别清洁区域、避开障碍物并规划路线，从而高效完成清洁任务。它们的优势包括 24/7 全天候运行、降低人工成本和提高清洁效率。然而，如何有效调度多辆无人驾驶保洁车，合理规划其保洁路径，以满足不同园区在不同时间的洁净需求，仍是一个紧迫的挑战。

In this context, establishing a mathematical model to optimize the scheduling and path planning of autonomous cleaning vehicles is particularly important. Through scientific task allocation and path optimization, it is possible to enhance the operational efficiency of the cleaning vehicles, reduce operational costs, and address challenges posed by unforeseen events. Ultimately, the goal is to achieve intelligent management of the campus environment, creating a cleaner and more comfortable learning and living space for students and faculty.
在这种情况下，建立一个数学模型来优化自动驾驶清洁车的调度和路径规划尤为重要。通过科学的任务分配和路径优化，可以提高清洁车的运营效率，降低运营成本，并应对意外事件带来的挑战。最终目标是实现校园环境的智能化管理，为学生和教职员工创造一个更清洁、更舒适的学习和生活空间。

Chongqing University’s Huxi Campus plans to introduce autonomous cleaning vehicles to improve the efficiency of environmental sanitation management. A mathematical model needs to be established to optimize the scheduling and routes of these cleaning vehicles.
重庆大学湖西校区计划引入无人驾驶清洁车，以提高环卫管理的效率。需要建立一个数学模型来优化这些清洁车的调度和路线。

https://mp.weixin.qq.com/s?__biz=MzA5MTU2MTcwNw==&mid=2653094179&idx=1&sn=171c9163a8752d09b9643a364c6607ad&chksm=8a7a1059e21f1fd4b748366d16437c462757f34667cbf80f7b29567ccae08bbaf75a5c67e537&mpshare=1&scene=23&srcid=1018Cqr4OZ2Y60g57pqZIQaa&sharer_shareinfo=4e26de04df6b5d416d5b7c5a62c70ca7&sharer_shareinfo_first=4e26de04df6b5d416d5b7c5a62c70ca7#rd

(1) The campus needs to be divided into multiple cleaning areas to facilitate task allocation for autonomous cleaning vehicles.
（1） 园区需要划分为多个保洁区域，以方便无人保洁车的任务分配。

(2) A task allocation model should be developed based on the cleaning areas to optimize the efficiency and time utilization of the cleaning vehicles.
（2） 应根据清扫区域制定任务分配模型，以优化清扫车的效率和时间利用率。

(3) An algorithm must be designed to plan efficient routes for the autonomous cleaning vehicles to cover all designated cleaning areas.
（3） 必须设计一种算法，为自动清洁车规划有效的路线，以覆盖所有指定的清洁区域。

(4) A dynamic scheduling algorithm should be designed to address the impact of unforeseen events (such as activities and weather changes) on cleaning tasks within the campus.
（4） 应设计动态调度算法，以解决不可预见的事件（例如活动和天气变化）对校园内清洁任务的影响。

(5) A mathematical model needs to be established to evaluate the operational costs and cleaning effectiveness of autonomous cleaning vehicles to determine their overall benefits in campus management.
（5） 需要建立一个数学模型来评估自动清洁车的运营成本和清洁效果，以确定它们在校园管理中的整体效益。

Problem E Optimal urban population size and employment structure
问题 E O城市人口规模和就业结构

With the continuous advancement of urbanization, the urban population size is getting larger and larger, and the survival and development of the urban population are facing many challenges, including survival needs, housing needs, education needs, medical needs, employment needs, public service needs, entertainment needs, etc.
随着城市化进程的不断推进，城市人口规模越来越大，城市人口的生存和发展面临诸多挑战，包括生存需求、住房需求、教育需求、医疗需求、就业需求、公共服务需求、娱乐需求等。

In order to meet the various needs of the urban population, a large amount of resources need to be invested, especially a large amount of human resources are needed, so that the development of the urban population also provides more diversified employment opportunities for the society, forming the employment structure of the population in various industries.
为了满足城市人口的各种需求，需要投入大量的资源，特别是需要大量的人力资源，这样城市人口的发展也为社会提供了更加多元化的就业机会，形成了各行业人口的就业结构。

Assuming that the urban population are all active and hardworking workers, with professional knowledge and skills in the required industries, they are efficient production labor after their survival and development needs are met.
假设城市人口都是积极勤奋的劳动者，在所需行业拥有专业知识和技能，那么在满足他们的生存和发展需求后，他们是高效的生产劳动力。

In order to determine the relationship between urban population size and employment structure, please establish mathematical models and answer the following questions:
为了确定城市人口规模与就业结构之间的关系，请建立数学模型并回答以下问题。

(1) Establish a mathematical model to describe the relationship between urban population size and population demand, and determine the quantitative relationship between urban population size and various demands;
（1） 建立数学模型来描述城市人口规模与人口需求之间的关系，并确定城市人口规模与各种需求之间的定量关系;

(2) Establish a mathematical model to describe the relationship between the number of practitioners and the number of products and services they provide, and determine the mathematical model of the number of employed people in each industry;
（2） 建立数学模型来描述从业者的数量与其提供的产品和服务数量之间的关系，并确定每个行业的就业人数的数学模型;

(3) Based on the urban population quantity model and population employment model established in (1) and (2), describe the distribution pattern of urban population among various industries;
（3） 基于（1）和（2）中建立的城市人口数量模型和人口就业模型，描述城市人口在各行业之间的分布格局;

(4) Based on the model established in (3), find the optimal urban size;
（4） 根据 （3） 中建立的模型，找到最优的城市规模;

(5) Based on the model established in (4), find the optimal population employment structure.
（5） 根据 （4） 中建立的模型，找到最优的人口就业结构。